To post and run is someone who makes a post, hits the Publish button and then never comes back to the site for hours, days, or weeks to answer comments.
Like if you never got a response back to this comment you just made until so much time had passed you didn't even remember you made the comment so long ago. That is someone who posts and runs.
You can read more details on the site for each one of these bullet points. That's why I put a link there